Back up to external hhd

When the program freezes, it doesn't necessarily mean that nothing is happening.  When you were in Task Manager did you take a look to see whether anything was happening.  In particular, you should take a look at the Performance tab and see whether there is any read/write activity on your hard drives.

My suggestion is that you start the backup process and leave your computer on overnight.

Also, do you have Auto Backups of the catalog on?  Are any being created? By default, they will be found in the following folder:  C:\ProgramData\Adobe\Elements Organizer\Catalogs\_AutoBackup_

How large is your catalog?  What do you mean when you say the process freezes?  Depending on the size of your catalog, the process can take several minutes, or even hours.

Have you ever had any hidden files in your catalog?  Even though you may think that you have no missing files, any that were hidden will not show up in the Find> All Missing Files dialog unless you have the View>Hidden Files menu filter set to Show All Files.

Things like this can sometimes be attirbuted to files with odd names or special characters in the names (%#&?) stuff like that. 

You should also just use the catalogue interface to back up your catalogues-   You have to do at least one full backup then you can do incremental backups.